Note sur les invariants du groupe affine

TL;DR

This paper proves that locally P-invariant C^1-functions on GL(n) are also locally G-invariant, extending to distributions, thus revealing invariance properties of functions under affine group actions.

Contribution

It establishes that local invariance under the affine subgroup implies local invariance under the entire group for C^1-functions and distributions.

Findings

C^1-functions locally P-invariant are locally G-invariant

Extension of invariance results to distributions

Weak form of Baruch's results on invariance

Abstract

In the paper, it is proved that any $C^{1}$-function on GL(n) which is locally $P$-invariant (here $P$ is the affine (sub)group of GL(n)) is locally $G$-invairant. There is also a statement for distributions (a very weak form of Baruch's results).